Are you the one I'm looking for?..

It depends on whether you're writing in a formal or informal register. If you want to get excruciatingly nitpicky, the second example is substandard because "for whom" belongs to the formal register, but contractions don't.

OK, I'll stop. The practical answer is they're both correct. Don't worry about it. The first is more casual and the second is more formal.

In a first-person POV narration, if you were the narrator (which you kind of are, being the author), which would you use?

I'd use the first.

caw

Language maven Charles Harrington Elster (What in the Word?) suggests that the difference between who and whom is lost on most, so the separate usage in language is no longer needed, go ahead an use who. Although, if you know the distinction, go for it.